Reviews and recommendations

We're in a US election year, and as is usual at such times there is some discussion about the fairness of the voting system.

If you ever have been (or wanted to be) involved in a school or office council which has to be elected by popular vote, you have a fair idea of the sort of considerations that have to be made.

Charles Lutwidge Dodgson sat in the bows of a rowing boat and heaved on the oars in time with another young man who sat in front of him.

With Einstein's publication of The Foundation of the General Theory of Relativity in 1916 our view of the nature of the Universe was forever altered.

If you were to seek out books that attempt to popularise maths among the innumerati, you would notice that most give a quick nod to the golden ratio.

It turns out your mum was wrong after all: you can judge a book by its cover. This book has a colourful, detailed, and tantalising cover adorned with portraits of people you may or may not know. Who are they, and what do they have to do with numbers at work, and the culture in which we live?

How do you do it? Horizontally from side to side, or perhaps criss-cross, producing a series of Xs running up your feet? Towards the end of The shoelace book, its author Burkard Polster raises a troubling question. Despite all the here-today, gone-tomorrow vagaries of fashion, and in spite of the huge variety of shoe styles available to us in this golden age of footwear, why does almost everyone lace their shoes in one of these two ways?

Ever wondered what mathematicians do all day? Finding Moonshine tells the story of a year in the life of the author, an Oxford professor known for his books, as well as radio and TV presentations of mathematics to the general public.

"Marvellous, surprising, crystal-clear, amazing, stimulating, delightful, fascinating" — this is how our reviewer described Nonplussed!, a book published last year by by the same author.

In their new book John Bryant and Chris Sangwin explore the complex problems and challenges facing engineers and mathematicians now and through the ages.

The Poincaré conjecture is one of the few mathematical results that has managed to catch the interest of the mainstream media.

This review looks at two books on one of the most important, and most difficult, open problems in mathematics: the Riemann hypothesis.